<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -type ultrawide band gap spinel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi mathvariant="normal">ZnGa</mml:mi> <mml:mn>2</mml:mn

Transparent oxide semiconductors face a fundamental challenge in achieving bipolar functionality due to inherent doping asymmetry. Spinel $\text{ZnG}{\text{a}}_{2}{\text{O}}_{4}$, traditionally $n$-type under oxygen-poor growth conditions, has recently been reported to exhibit $p$-type semiconductivity at elevated temperatures through the proposed formation of $\mathrm{Z}{\mathrm{n}}_{\mathrm{Ga}}$ antisite acceptors. In this work, we systematically reevaluate the feasibility of $p$-type semiconductivity in $\text{ZnG}{\text{a}}_{2}{\text{O}}_{4}$ by theoretically examining its electronic band structure and defect thermodynamics. The valence band maximum is primarily composed of deep and localized O $2p$ orbitals, severely impeding hole generation and transport. Furthermore, defect thermodynamics reveal a self-regulating compensation mechanism driven by cation antisites---$\mathrm{G}{\mathrm{a}}_{\mathrm{Zn}}$ donors and $\mathrm{Z}{\mathrm{n}}_{\mathrm{Ga}}$ acceptors. This mechanism intrinsically pins the Fermi level (${E}_{\mathrm{F}}$) from mid-gap through the $n$-type region under all growth conditions. Crucially, $\mathrm{G}{\mathrm{a}}_{\mathrm{Zn}}$ donors exhibit negative formation energies across the $p$-type ${E}_{\mathrm{F}}$ range, triggering autocompensation that blocks extrinsic $p$-type doping. Experimental claims of high-temperature $p$-type behavior are undermined by inconsistencies in ${E}_{\mathrm{F}}$ measurements and unverified independently. Later proposed Zn-rich alloys $(\mathrm{Z}{\mathrm{n}}_{(1+2x)}\mathrm{G}{\mathrm{a}}_{2(1\ensuremath{-}x)}{\mathrm{O}}_{4})$ with intermediate bands---intended to explain purported conductivity---are thermodynamically unstable ($\ensuremath{\Delta}H$ = \ensuremath{-}57.4 meV/atom) and exhibit unobserved sub-band-gap states. These findings confirm $\text{ZnG}{\text{a}}_{2}{\text{O}}_{4}$'s fundamental incompatibility with $p$-type functionality, necessitating rigorous experimental validation for viable $p$-type ultrawide band gap semiconductors.